In a previous report [G. Weill, Propagation of Electromagnetic Waves along Corrugated Lines, ASTIA Document AD 115 049] an approximate formula for the constant of propagation has been derived from an exact integral equation. It is the purpose of this report to check experimentally the accuracy of our formula

Kuehl, Hans

Weill, Georges G.

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AFOSR-TN-57-786
ASTIA Document No. AD 148 017
CALIFORNIA INSTITUTE OF TECHNOLOGY
Antenna Laboratory
Technical Report No. 13
ELECTROMAGNETIC WAVES ON CORRUGATED LINES: 
PROPAGATION CONSTANT MEASUREMENTS
Georges G. Weill 
Hans Kuehl
This research was supported by the U.S. Air Force 
through the Air Force Office of Scientific Research 
of the Air Research and Development Command, under 
Contract No. AFl8(600)-1113. Reproduction in whole 
or in part is permitted for any purpose of the 
United States Government.
Qualified requestors may obtain copies of this re­
port from the ASTIA Document Service Center, Dayton 
2, Ohio. Department of Defense contractors must be 
established for ASTIA services or have their "need- 
to-know" certified by the cognizant military agency 
of their project or contract.
ELECTROMAGNETIC WAVES ON CORRUGATED LINES: 
PROPAGATION CONSTANT MEASUREMENTS
Georges G. Weill 
Hans Kuehl
I. Introduction
In a previous report(1) an approximate formula for the constant of 
propagation has been derived from an exact integral equation. It is the 
purpose of this report to check experimentally the accuracy of our formula.
Figure 1.
(1)G. Weill, Propagation of Electromagnetic Waves along Corrugated Lines, 
(ASTIA Document AD115 049).
2.
Let us recall first that the corrugated line under consideration is
made of parallel "infinite" metallic strips. (Figure 1). The strips have
length ℓ, spacing d . They are supposed to be infinite in the direction
of the axis y, and the line itself is infinite in the direction of the x
axis. We are considering here the TM symmetric case (Hy, Ex, Ez). With 
and we obtained the integral equation:
L*+ and L*- have been defined in (1).
A residue expansion gives us an infinite system of linear equations. 
Taking the first term of the first equation, the only significant one, we get:
Equating the arguments of both sides we get a relation
we defined the unilateral Fourier transforms:
Putting
3.
Curves have been drawn for
K = 1/10 : 10 strips per wavelength 
K = 1/3     :         3 strips per wavelength
(See Figures 2 and 3.)
II. Experimental Device.
For the sake of convenience, measurements have been made at microwave 
frequencies (S band). To measure the propagation constant of the surface 
wave we used a long "corrugated line". The length of the strips is great 
compared to their width. The launching of the surface wave is operated by 
means of a sectoral horn; the other end of the line radiates freely.
To avoid perturbation by the launching device or by end effects, mea­
surements have taken place in the middle section of the line.
The experimental device is schematized on Figure 4 and represented in 
Figure 5.
III. Measurement Method.
We compare the phase of the wave propagated on the corrugated line 
with the phase of a reference wave propagated in a waveguide. The carriage 
of the slotted line is moved to get a zero on the detector. Then, any
the relation becomes
Equipment
UHF signal generator HP model 616A
TWT amplifier HP model 491A
Detector HP model 415B
Slotted line HP model 5810A
Variable attenuator HP model S375.
4.
Figure 2.
SY
M
M
ET
R
IC
 CA
SE
5.
Figure 3.
SY
M
M
ET
R
IC
 CAS
E
6.
Fi
gu
re
 4.
7.
Figure 5
8.
displacement of n λg (n integer; λg guided wavelength) of the probe 
gives us a zero on the detector meter.
The accuracy which can be expected from the method, taking n = 5 
is about 5%.
ℓ cm L λg cm  Γ measured
Γ 
theoretical
1.10 .70 9.8 .10 .10
2.10 1.32 8.8 .11 .115
3.60 2.26 5.4 .18 .185
4.10 2.56 4.0 .25 .250
4.38 2.75 3.0 .33 .335
4.80 3.02 9.5
K = 1/3 d = 3 cm f = 3333 mc
ℓ cm L λg cm Γ measured
Γ 
theoretical
1.43 1.00 8.9 .35 .335
2.10 1.47 8.5 .35 .355
2.58 1.80 7.7 .39 .390
2.86 2.0 6.5 .46 .435
3.6 2.51 8.8
IV. Experimental Results.
To be able to use a smaller set of strips, measurements have been 
made at f1 = 3000 mc/s for K = 1/10, and f2 = 3333 mc/s for K = 1/3. 
The results, summarized in the following tables are represented on Figures 
2 and 3, showing a very good agreement with the theoretical ones.
K = .1 d = 1 cm f = 3000 mc
9.
We have checked points in the non-transmitting band of the structure. 
We get, as predicted, no guided wavelength but merely the primary excitation 
wave. (Points 4.80 and 3.6).
V. Conclusion.
The approximate formula for L = f [Γ, κ] obtained from our integral 
equation shows a quite good agreement with experiment; now further approxi­
mation seems to be needed, at least for engineering purposes.
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Electromagnetic Waves on Corrugated Lines: Propagation Constant Measurements

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Electromagnetic Waves on Corrugated Lines: Propagation Constant Measurements

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